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Uncertainty and negation—Information theoretic applications
Author(s) -
Srivastava Amit,
Kaur Lakhveer
Publication year - 2019
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22094
Subject(s) - negation , divergence (linguistics) , event (particle physics) , probability distribution , mathematics , entropy (arrow of time) , kullback–leibler divergence , probability measure , computer science , statistics , linguistics , programming language , philosophy , physics , quantum mechanics
The negation of a probability distribution developed by Yager and Liu deals with the uncertainty when the probability of a particular event is equally distributed among the other alternatives. In this case, intuitively the uncertainty associated with that particular event should be equally distributed among the uncertainty associated with the other alternatives. However, for verifying this, we need to develop uncertainty measures that will measure the uncertainty associated with the negation of a probability distribution. In the present study, we have developed measures analogous to the well known Shannon entropy function and the Kullback Leibler’s divergence for determining the uncertainty related with the negation and studied its properties. Finally, we have derived the Baye’s thoerem associated with the negation of probabilities of a sequence of events.